instruments of development: randomization in the tropics,

8/14/2019 Instruments of Development: Randomization in the Tropics,

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Instruments of development:

Randomization in the tropics, and the search for the elusive keys to economic

development

Angus Deaton

Research Program in Development Studies

Center for Health and WellbeingPrinceton University

January, 2009

The Keynes Lecture, British Academy, October 9th, 2008. I am grateful to Abhijit

Banerjee, Tim Besley, Anne Case, Hank Farber, Bill Easterly, Bo Honor, Michael

Kremer, David Lee, Chris Paxson, Sam Schulhofer-Wohl, Burt Singer, Jesse Rothstein,and John Worrall for helpful discussions in the preparation of this paper. For comments

on a draft, I would like to thank Tim Besley, Richard Blundell, David Card, Winston Lin,

John List, Costas Meghir, David McKenzie, Burt Singer, Alessandro Tarozzi, Gerard van

den Berg, Eric Verhoogen and especially Esther Duflo. I also like to acknowledge aparticular intellectual debt to Nancy Cartwright, who has discussed these issues patiently

with me for several years, whose own work on causality has greatly influenced me, and

who pointed me towards other important work; to Jim Heckman, who has long thoughtdeeply about the issues in this lecture, and many of whose views are recounted here; and

to David Freedman, whose recent death has deprived the world of one of its greatest

statisticians, and who consistently and effectively fought against the (mis)use oftechnique as a substitute for substance and thought. None of which removes the need for

the usual disclaimer, that the views expressed here are entirely my own. I acknowledge

financial support from NIA through grant P01 AG0584214 to the National Bureau ofEconomic Research. (Minor revisions, March 1st, 2009).


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Instruments of development:

Randomization in the tropics, and the search for the elusive keys to economic

development

Angus Deaton

ABSTRACT

There is currently much debate about the effectiveness of foreign aid and about what kind

of projects can engender economic development. There is skepticism about the ability of

econometric analysis to resolve these issues, or of development agencies to learn from

their own experience. In response, there is movement in development economics towards

the use of randomized controlled trials (RCTs) to accumulate credible knowledge of what

works, without over-reliance on questionable theory or statistical methods. When RCTs

are not possible, this movement advocates quasi-randomization through instrumental

variable (IV) techniques or natural experiments. I argue that many of these applicationsare unlikely to recover quantities that are useful for policy or understanding: two key

issues are the misunderstanding of exogeneity, and the handling of heterogeneity. I

illustrate from the literature on aid and growth. Actual randomization faces similar

problems as quasi-randomization, notwithstanding rhetoric to the contrary. I argue that

experiments have no special ability to produce more credible knowledge than other

methods, and that actual experiments are frequently subject to practical problems that

undermine any claims to statistical or epistemic superiority. I illustrate using prominent

experiments in development. As with IV methods, RCT-based evaluation ofprojects is

unlikely to lead to scientific progress in the understanding of economic development. I

welcome recent trends in development experimentation away from the evaluation of

projects and towards the evaluation of theoretical mechanisms.

KEYWORDS: Randomized controlled trials, instrumental variables, development,

foreign aid, growth, poverty reduction


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1. Introduction

The effectiveness of development assistance is a topic of great public interest. Much of

the public debate among non-economists takes it for granted that, if the funds were made

available, development would follow, Pogge (2005), Singer (2004), and at least some

economists agree, Sachs (2005, 2008). Others, most notably Easterly (2006), are deeply

skeptical, a position that has been forcefully argued at least since Bauer (1971, 1981).

Few academic economists or political scientists agree with Sachs views, but there is a

wide range of intermediate positions, recently well assembled by Easterly (2008). The

debate runs the gamut from the macrocan foreign assistance raise growth rates and

eliminate poverty?to the microwhat sorts of projects are likely to be effective?

should aid focus on electricity and roads, or on the provision of schools and clinics or

vaccination campaigns? In this lecture, I shall be concerned with both the macro and

micro kinds of assistance. I shall have very little to say about what actually works and

what does not; but it is clear from the literature that we do not know. Instead, my main

concern is with how we should go about finding out whether and how assistance works

and with methods for gathering evidence and learning from it in a scientific and

cumulative way. I am not an econometrician, but I believe that econometric

methodology needs to be assessed, not only by methodologists, but by those who are

concerned with the substance of the issue. Only they (we) are in a position to tell when

something has gone wrong with the application of econometric methods, not because

they are incorrect given their assumptions, but because their assumptions do not apply, or

because they are incorrectly conceived for the problem at hand. Or at least that is my

excuse for meddling in these matters.


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Any analysis of the extent to which foreign aid has increased economic growth in

recipient countries immediately confronts the familiar problem of simultaneous causality;

the effect of aid on growth, if any, will be disguised by effects running in the opposite

direction, from poor economic performance to compensatory or humanitarian aid. It is

not immediately obvious how to disentangle these effects, and some have argued that the

question is not answerable and that econometric studies of it should be abandoned.

Certainly, the econometric studies that use international evidence to examine aid

effectiveness currently have low professional status. Yet it cannot be right to give up on

the issue. There is no general or public understanding that nothing can be said, and to

give up the econometric analysis is simply to abandon precise statements for loose and

unconstrained histories of episodes selected to support the position of the speaker.

The analysis of aid effectiveness typically uses cross-country growth regressions with

the simultaneity between aid and growth dealt with using instrumental variable methods.

I shall argue in the next section that there has been a good deal of misunderstanding in

the literature about the use of instrumental variables. Econometric analysis has changed

its focus over the years, away from the analysis of models derived from theory towards

much looser specifications that are statistical representations of program evaluation. With

this shift, instrumental variables have moved from being solutions to a well-defined

problem of inference to being devices that induce quasi-randomization. Old and new

understandings of instruments co-exist, leading to errors, misunderstandings and

confusion, as well as unfortunate and unnecessary rhetorical barriers between disciplines

working on the same problems. These abuses of technique have contributed to a general

skepticism about the ability of econometric analysis to answer these big questions.


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A similar state of affairs exists in the microeconomic area, in the analysis of the

effectiveness of individual programs and projects, such as the construction of

infrastructuredams, roads, water supply, electricityand in the delivery of services

for example for education, health or policing. There is great frustration with aid

organizations, particularly the World Bank, for allegedly failing to learn from its projects

and to build up a systematic catalog of what works and what does not. In addition, some

of the skepticism about macro econometrics extends to micro econometrics, so that there

has been a movement away from such methods and towards randomized controlled trials.

According to Esther Duflo, one of the leaders of the new movement in development,

Creating a culture in which rigorous randomized evaluations are promoted, encouraged,

and financed has the potential to revolutionize social policy during the 21st

century, just

as randomized trials revolutionized medicine during the 20th. This quote is from a 2004

Lancet editorial headed The World Bank is finally embracing science.

In Section 4 of this paper, I shall argue that in ideal circumstances, randomized

evaluations of projects are useful for obtaining a convincing estimate of the average

effect of a program or project. The price for this success is a focus that is too narrow to

tell us what works in development, to design policy, or to advance scientific knowledge

about development processes. Project evaluation using randomized controlled trials is

unlikely to discover the elusive keys to development, nor to be the basis for a cumulative

research program that might progressively lead to a better understanding of development.

This argument applies a fortiori to instrumental variables strategies that are aimed at

generating quasi-experiments; the value of econometric methods cannot be assessed by

how closely they approximate randomized controlled trials. Following Cartwright


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(2007a, b), I argue that evidence from randomized controlled trials has no special

priority. Randomization is not a gold standard because there is no gold standard,

Cartwright (2007a.) Randomized controlled trials cannot automatically trump other

evidence, they do not occupy any special place in some hierarchy of evidence, nor does it

make sense to refer to them as hard while other methods are soft. These rhetorical

devices are just that; a metaphor is not an argument.

More positively, I shall argue that the analysis of projects needs to be refocused

towards the investigation of potentially generalizable mechanisms that explain why and

in what contexts projects can be expected to work. The best of the experimental work in

development economics already does so, because its practitioners are too talented to be

bound by their own methodological prescriptions. Yet there would be much to be said for

doing so more openly. I concur with the general message in Pawson and Tilley (1997),

who argue that thirty years of project evaluation in sociology, education and criminology

was largely unsuccessful because it focused on whetherprojects work instead of on why

they work. In economics, warnings along the same lines have been repeatedly given by

James Heckman, see particularly Heckman (1992) and Heckman and Smith (1995), and

much of what I have to say is a recapitulation of his arguments.

The paper is organized as follows. Section 2 lays out some econometric preliminaries

concerning instrumental variables and the vexed question of exogeneity. Section 3 is

about aid and growth. Section 4 is about randomized controlled trials. Section 5 is about

using empirical evidence and where we should go next.


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2. Instruments, identification, and the meaning of exogeneity

It is useful to begin with a simple and familiar econometric model that I can use to

illustrate the differences between different flavors of econometric practice; this has

nothing to do with economic development, but has the virtue of simplicity and is easy to

contrast with the development practice that I wish to discuss. In contrast to the models

that I will discuss later, I think of this as a model in the spirit of the Cowles Foundation.

It is the simplest possible Keynesian macroeconomic model of national income

determination taken from once-standard econometrics textbooks. There are two equations

which together comprise a complete macroeconomic system. The first equation is a

consumption function, in which aggregate consumption is a linear function of aggregate

national income, while the second is the national income accounting identity that says

that income is the sum of consumption and investment. I write the system in standard

notation as

C Y u = + + (1)

Y C I + (2)

According to (1), consumers choose the level of aggregate consumption with reference to

their income, while in (2), investment is set by the animal spirits of entrepreneurs in a

way that is outside of the model. No modern macroeconomist would take this model

seriously, though the simple consumption function is clearly an ancestor of more

satisfactory and complete modern formulations; in particular, we can think of it (or at

least its descendents) as being derived from a coherent model of intertemporal choice.

Similarly, modern versions would postulate some theory for what determines investment


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I; here it is simply taken as given, and assumed to be orthogonal to the consumption

disturbance u.

In this model, consumption and income are simultaneously determined so that, in

particular, a stochastic realization ofuconsumers displaying animal spirits of their

ownwill affect not only C, but also Ythrough equation (2), so that there is a positive

correlation between Cand Y. As a result, ordinary least squares estimation of (1) will

lead to upwardly biased and inconsistent estimates of the parameter .

This simultaneity problem can be dealt with in a number of ways. One is to solve (1)

and (2), to get the reduced form equations

1 1 1

uC I

= + +

(3)

1 1 1

I uY

= + +

(4)

Either of these equations can be consistently estimated by OLS, and it is easy to show

that the same estimates of and will be obtained from either one. An alternative

method of estimation is to focus on the consumption function (1), and to use our

knowledge of (2) to note that investment can be used as an instrumental variable (IV) for

income. In the IV regression, there is a first stage regression in which income is

regressed on investment; this is identical to equation (4), which is part of the reduced

form. In the second stage, consumption is regressed on the predicted value of income

from (4). In this simple case, the IV estimate of is identical to the estimate from the

reduced form. This simple model may not be a very good model, but it is a model, if only

a primitive one.


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I now leap forward sixty years, and consider an apparently similar set up, again using

an absurdly simple specification. The World Bank (let us imagine) is interested in

whether to advise the government of China to build more railway stations. The Bank

economists write down an econometric model in which the poverty head count ratio in

city c is taken to be a linear function of an indicatorR of whether or not the city has a

railway station,

c c cP R v = + + (5)

where (I hesitate to call it a parameter) indicates the effectpresumably negativeof

infrastructure (here a railway station) on poverty. While we cannot expect to get useful

estimates of from OLS estimation of (5)railway stations may be built to serve more

prosperous cities, they are rarely built in deserts where there are no people, or there may

be third factors that influence boththis is seen as a technical problem for which

there is a wide range of econometric treatments including, of course, instrumental

variables.

We no longer have the reduced form of the previous model to guide us but if we can

find an instrumentZthat is correlated with whether a town has a railway station, but

uncorrelated with v, we can do the same calculations and obtain a consistent estimate. For

the record, I write this equation

c c cR Z = + + (6)

Good candidates forZmight be indicators of whether the city has been designated by the

Government of China as belonging to a special infrastructure development area, or

perhaps an earthquake that conveniently destroyed a selection of railway stations, or even


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the existence of river confluence near the city, since rivers were an early source of power,

and railways served the power-based industries. I am making fun, but not much.

My main argument is that the two econometric structures, in spite of their

resemblance and the fact that IV techniques can be used for both, are in fact quite

different. In particular, the IV procedures that work for the effect of national income on

consumption are unlikely to give useful results for the effect of railway stations on

poverty. To explain the differences, I begin with the language. In the original example,

consumption and income are treated symmetrically, and appear as such in the reduced

form equations (3) and (4). In contemporary examples, such as the railways, there is no

symmetry. Instead, we have a main equation (5), which used to be the structural

equation (1). We also have a first-stage equation, which is the regression of railway

stations on the instrument, which was previously just one of the equations in the reduced

form. The reduced form, of course, was typically more completely specified than the

first-stage regression, since it was derived from a notionally complete model of the

system. The now rarely considered regression of the variable of interest on the

instrument, here of poverty on earthquakes or on river confluences, is nowadays referred

to as the reduced form, although it was originally one equation of a multiple equation

reduced form within which it had no special significance. These language shifts

sometimes cause confusion, but they are not the most important differences between the

two systems.

The crucial difference is that the relationship between railways and poverty is not a

model at all, unlike the consumption model which embodied a(n admittedly crude) theory

of income determination. While it is clearlypossible that the construction of a railway


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station will reduce poverty, there are many possible mechanisms, some of which will

work in one context and not in another. In consequence is unlikely to be constant over

different cities, nor can its variation be usefully thought of as random variation that is

uncorrelated with anything else of interest. Instead, it is precisely the variation in that

encapsulates the poverty reduction mechanisms that ought to be the main objects of our

enquiry. Instead, the equation of interest is thought of as a representation of something

more akin to an experiment or a biomedical trial, in which some cities get treated with

a station, and some do not. The role of econometric analysis is not, as in the Cowles

example, to estimate and investigate a casual model, but to create an analogy, perhaps

forced, between an observational study and an experiment, Freedman (2006, 691).

One immediate task is to recognize and somehow deal with the variation in , which

is typically referred to as the heterogeneity problem in the literature. The obvious way

is to define a parameter of interest in a way that corresponds to something we want to

know for policy evaluationperhaps the average effect on poverty over some group of

citiesand then devise an appropriate estimation strategy. However, this step is often

skipped in practice, perhaps because of a mistaken belief that (5) is a structural equation

in which is a constant, so that the analysis can go immediately to the choice of

instrumentZ, over which a great deal of imagination is often exercised. As in the

traditional model, the instrument is selected to satisfy two criteria, that it be correlated

with cR and uncorrelated with .cv Of course, if heterogeneity is indeed present, the

probability limit of the IV estimator will in general depend on the choice of instrument,

Heckman (1997). Such a procedure is the opposite of standard statistical practice, in

which a parameter of interest is defined first, followed by an estimator that delivers that


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parameter. Instead, we have a procedure in which the choice of the instrument, which is

guided by criteria designed for a different situation, is implicitly allowed to determine the

parameter of interest. This goes beyond the old story of looking an object where the light

is strong enough to see; rather, we have control over the light, but choose to let it fall

where it may, and then proclaim that whatever it illuminates is what we were looking for

all along.

Recent econometric analysis has given us a more precise characterization of what we

can expect from such a method. In the railway example, where the instrument is the

designation of a city as belonging to the special infrastructure zone, the probability

limit of the IV estimator is the average of poverty reduction effects over those cities who

were induced to construct a railway station by being so designated. This averages is

known as the local average treatment effect (LATE), and its recovery by IV estimation

requires a number of non-trivial conditions including, for example, that no cities who

would have constructed a railway station are perverse enough to be actually deterred

from doing so by the positive designation, see Angrist and Imbens (1994), who

established the LATE theorem. The LATE may, or may not, be a parameter of interest to

the World Bank or the Chinese government and in general, there is no reason to suppose

that it will be. For example, the parameter estimated will typically notbe the average

poverty reduction effect over the designated cities, nor the average effect over all cities.

I find it hard to make any sense of the LATE. We are unlikely to learn much about

the processes at work if we refuse to say anything about what determines;

heterogeneity is not a technical problem calling for an econometric solution, but is a

reflection of the fact that we have not started on our proper business, which is trying to


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understand what is going on. Of course, if we are as skeptical of the ability of economic

theory to deliver useful models as are many applied economists today, the ability to avoid

modeling can be seen as an advantage, though it should not be a surprise when such an

approach provides answers that are hard to interpret.

There is a related issue that bedevils a good deal of contemporary applied work,

which is the understanding ofexogeneity, a word that I have so far avoided. Suppose, for

the moment, that the effect of railway stations on poverty is the same in all cities, and we

are looking for an instrument, which is required to be exogenous in order to consistently

estimate. According to Merriam-Websters dictionary, exogenous means caused by

factors or an agent from outside the organism or system, and this common usage is often

employed in applied work. However, the consistency of IV estimation requires that the

instrument be orthogonal to the error term v in the equation of interest, which is not

implied by the Merriam-Webster definition, see Leamer (1985, p. 260). Heckman (2000)

suggests using the term external (which he traces back to Wright and Frisch in the

1930s) for the Merriam-Webster definition, for variables whose values are not set or

caused by the variables in the model (according to this, consumption and investment are

internal variables, and investment an external variable), and keeping exogenous for

the orthogonality condition that is required for consistent estimation in this instrumental

variable context. The terms are hardly standard, but I adopt them here because I need to

make the distinction. The main issue, however, is not the terminology, but that the two

concepts be kept distinct, so that we can see when the argument being offeredis a

justification for externality when what is requiredis exogeneity. An instrument that is


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external, but not exogeneous, will not yield consistent estimates of the parameter of

interest, even when that parameter is constant.

Failure to separate externality and endogeneity has caused, and continues to cause,

endless confusion in the applied development (and other) literatures. Natural or

geographic variablesdistance from the equator (as an instrument for per capita GDP in

explaining religiosity, McCleary and Barro, 2006), rivers (as an instrument for the

number of school districts in explaining educational outcomes, Hoxby, 2000), land

gradient (as an instrument for dam construction in explaining poverty, Duflo and Pande,

2007), month of birth as an instrument for years of schooling in an earnings regression,

Angrist and Krueger, 1991, or rainfall as an instrument for economic growth in

explaining civil war, Miguel, Satyanath, and Sergenti, 2004, and the examples could be

multiplied ad infinitum)are not affected by the variables being explained, and are

clearly external. So are historical variablesthe mortality of colonial settlers is not

influenced by current institutional arrangements in ex-colonial countries, Acemoglu,

Johnson, Robinson (2001), nor does the countrys growth rate today influence which

country they were colonized by, Barro 1998. Whether any of these instruments is

exogenous depends on the nature of the equation of interest, and is not guaranteed by its

externality. And because exogeneity is an identifying assumption that must be made prior

to analysis of the data, no empirical tests are possible. This does not prevent many

attempts in the literature, often by misinterpreting a satisfactory overidentification test as

evidence for valid identification. Such tests can tell us whether estimates change when we

select different subsets from a set of possible instruments. While the test is clearly


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informative, acceptance is consistent with all of the instruments being invalid, while

failure is consistent with a subset being correct.

In my running example, earthquakes and rivers are external to the system, and are not

caused by poverty nor by the construction of railway stations, and the designation as an

infrastructure zone may also be determined by factors independent of poverty or

railways. But even earthquakes (or rivers) are not exogenous if they have an effect on

poverty other than through their destruction (or encouragement) of railway stations, as

will almost always be the case. The absence of simultaneity does not guarantee

exogeneity; exogeneity requires the absence of simultaneity, but is not implied by it.

Even random numbersthe ultimate external variablesmay be endogenous, at least in

the presence of heterogeneity. Again, the example comes from Heckmans (1997)

discussion of Angrists (1990) famous use of draft lottery numbers as an instrumental

variable in his analysis of the subsequent earnings of Vietnam veterans.

I can illustrate Heckmans argument using the Chinese railways example with the

zone designation as instrument. Rewrite the equation of interest, (5), as

{ ( ) }c c c c c c

P R w R v R = + + = + + + (7)

wherec

w is defined by the term in curly brackets, and is the mean of over the cities

that get the station so that the compound error term w has mean zero. Suppose the

designation as an infrastructure zone isc

D , which takes values 1 or 0, and that the

Chinese bureaucracy, persuaded by young development economists, decides to

randomize and sets the designation of cities by flipping a Yuan. For consistent estimation

of , we want the covariance of the instrument with the error to be zero. The covariance

is


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( ) [( ) ] [( ) | 1, 1] ( 1, 1)c cE D w E RD E D R P D R = = = = = = (8)

which will be zero if either (a) the average effect of building a railway station on poverty

among the cities induced to build one by the designation is the same as the average effect

among those who would have built one anyway, or (b) no city not designated builds a

railway station1. If (b) is not guaranteed byfiat, we cannot suppose that it will otherwise

hold, and we might reasonably hope that among the cities who build railway stations,

those induced to do so by the designation are those where there is the largest effect on

poverty, which violates (a). In the example of the Vietnam veterans, the instrument (the

draft lottery number) fails to be exogenous because the error term in the earnings

equation depends on each individuals rate of return to schooling, and whether or not

each potential draftee accepted their assignmenttheir veterans statusdepends on that

rate of return. In practice, most instruments are not random numbers, and the assumption

that the instrument is orthogonal toc

, which is accepted in (8), will also have to be

defended.

The general lesson here is once again the ultimate futility of trying to avoid thinking

about how and why things work; if we do not do so, we are left with undifferentiated

heterogeneity that is likely to prevent consistent estimation of any parameter of interest.

One appropriate response is to specify exactly how cities respond to their designation, an

approach that leads to Heckmans local instrumental variable methods, Heckman and

Vytlacil (1999, 2007), Heckman, Urzua and Vytlacil (2006). Similar questions are

pursued in van den Berg (2008).

1 I am grateful to Winston Lin for clarification on this point.


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3. Instruments of development

The question of whether aid has helped economies grow faster is typically asked within

the framework of standard growth regressions. These regressions use data for many

countries over a period of years, usually from the Penn World Table, the current version

of which provides data on real per capita GDP and its components in purchasing power

dollars for more than 150 countries as far back as 1950. The model to be estimated has

the rate of growth of per capita GDP as the dependent variable, while the explanatory

variables include the lagged value of GDP per capita, the share of investment in GDP,

and measures of the educational level of the population, see for example Barro and Sala-

i-Martin (1995, Chapter 12) for an overview. Other variables are often added, and my

main concern here is with one of these, external assistance (aid) as a fraction of GDP. A

typical specification can be written

1 0 1 2 3 4ln lnct

ct ct ct ct ct ct

ct

IY Y H Z A u

Y

+ = + + + + + + (9)

where Yis per capita GDP,Iis investment,His a measure of human capital or education,

andA is the variable of interest, aid as a share of GDP.Zstands for whatever other

variables are included. The index c is for country and tfor time. Growth is rarely

measured on a year to year basisthe data in the Penn World Table are not suitable for

annual analysisso that growth may be measured over ten, twenty, or forty year

intervals. With around forty years of data, there are four, two, or one observation for each

country.

An immediate question is whether the growth equation (9) is a model-based Cowles-

type equation, as in my national income example, or whether it is more akin to the

atheoretical analyses in my invented Chinese railway example. There are elements of


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both here. If we ignore theZandA variables in (9), the model can be thought of as a

Solow growth model, extended to add human capital to physical capital, see again Barro

and Sala-i-Martin, who derive their empirical specifications from the theory, and also

Mankiw, Romer, and Weil (1992), who extended the Solow model to include education.

However, the addition of the other variables, including aid, is typically less well justified.

In some cases, for example under the assumption that all aid is invested, it is possible to

calculate what effect we might expect aid to have, see Rajan and Subramanian (2005). If

we follow this route, (9) would not be usefulbecause aid is already includedand we

should instead investigate whetheraid is indeed invested, and then infer the effectiveness

of aid from the effectiveness of investment. Even so, it presumably matters what kind of

investment is promoted by aid, and aid for roads, for dams, for vaccination programs, or

for humanitarian purposes after an earthquake are likely to have different effects on

subsequent growth. More broadly, one of the main issues of contention in the whole

debate is what aid actually does. Just to list a few of the possibilities, does aid increase

investment, does aid crowd out domestic investment, is aid stolen, or does aid create rent-

seeking that undercuts the long-run conditions for growth? Once all of these possibilities

are admitted, it is clear that the analysis of (9) is not a Cowles model at all, but is seen as

some sort of biomedical experiment in which different countries are dosed with

different amounts of aid, and we are trying to measure the average response. As in the

Chinese railways case, a regression such as (9) will not give us what we want, because

the doses of aid are not randomly administered to different countries, so our first task is

to find an instrumental variable that will generate quasi-randomness.


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The most obvious problem with a regression of aid on growth is the simultaneous

feedback from growth to aid that is generated by humanitarian responses to economic

collapse or to natural or man-made disasters that engender economic collapse. More

generally, aid flows from rich countries to poor countries, and poor countries, by

definition, are those with poor records of economic growth. This feedback, from low

growth to high aid, will obscure, nullify, or reverse any positive effects of aid. Most of

the literature attempts to eliminate this feedback by using one or more instrumental

variables and, although they would not express it in these terms, the aim of the

instrumentation is to a restore a situation in which the pure effect of aid on growth can be

observed, as if in a randomized situation. How close we get to this ideal depends, of

course, on the choice of instrument.

Although there is some variation across studies, there is a standard set of instruments,

originally proposed by Boone (1996), which include the log of population size and

various country dummies, for example, a dummy for Egypt, or for francophone West

Africa. One or both of these instruments are used in almost all the papers in a large

subsequent literature, including Burnside and Dollar (2000), Hansen and Tarp (2000,

2001), Dalgaard and Hansen (2001), Guillamont and Chauvet (2001), Lensink and White

(2001), Easterly, Levine, and Roodman (2003), Dalgaard, Hansen, and Tarp (2004),

Clemens, Radelet, and Bhavani (2004), Rajan and Subramanian (2005), and Roodman

(2008). The rationale for population size is that larger countries get less aid per capita,

because the aid agencies allocate aid on a country basis, with less than full allowance for

population size. The rationale for what I shall refer to as the Egypt instrument is that

Egypt gets a great deal of American aid as part of the Camp David accords in which it


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agreed to a partial rapprochement with Israel. The same argument applied to the

francophone countries, which receive additional aid from France because of their past

colonial status. By comparing these countries with countries not so favored, or by

comparing populous with less populous countries, we can observe a kind of variation in

the share of aid in GDP that is unaffected by the negative feedback from poor growth to

compensatory aid. In effect, we are using the variation across populations of different

sizes as a natural experiment to reveal the effects of aid.

If we examine the effects of aid on growth without any allowance for reverse

causality, for example by estimating equation (9) by ordinary least squares, the estimated

effect is typically negative. For example, Rajan and Subramanian (2005), in one of the

most careful recent studies, find that an increase in aid by one percent of GDP comes

with a reduction in the growth rate of one tenth of a percentage point a year. Easterly

(2005) paints with a broader brush, and provides many other (sometimes spectacular)

examples of negative associations between aid and growth. When instrumental variables

are used to eliminate the reverse causality, Rajan and Subramanian find a weak or zero

effect of aid, and contrast that finding with the robust positive effects of investment on

growth in specifications like (9). I should note although Rajan and Subramanians study

is an excellent one, it is certainly not without its critics, and as the authors note, there are

many difficult econometric problems beyond the choice of instruments, including how to

estimate dynamic models with country fixed effects on limited data, the choice of

countries and sample period, the type of aid that needs to be considered, and so on.

Indeed, it is those other issues that are the focus of most of the literature cited above. The

substance of this debate is far from over.


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My main concern here is with the use of the instruments, what they tell us, and what

they might tell us. The first point is that neither the Egypt nor the population instrument

are plausibly exogenous; both are externalCamp David is not part of the model, nor

was it caused by Egypts economic growth, and similarly for population sizebut

exogeneity would require that neither Egypt nor population size have any influence on

economic growth except through the effects on aid flows, which makes no sense at all.

We also need to recognize the heterogeneity in the aid responses, and try to think about

how the different instruments are implicitly choosing different averages, involving

different weightings of countries. Or we could stop right here, conclude that there are no

valid instruments, and that the aid to growth question is not answerable in this way. I

shall argue otherwise, but I should also note that similar challenges over the validity of

instruments have become routine in applied econometrics, leading to widespread

skepticism by some, while others press on undaunted in an ever more creative search for

exogeneity.

Yet consideration of the instruments is not without value, especially if we move away

from instrumental variable estimation, with the use of instruments seen as technical, not

substantive, and think about the reduced form which contains substantive information

about the relationship between growth and the instruments. For the case of population

size, we find that, conditional on the other variables, population size is unrelated to

growth, which is one of the reasons that the IV estimates of the effects of aid are small or

zero. This (partial) regression coefficient is a much simpler object than is the instrumental

variable estimate; under standard assumptions, it tells us how much faster large countries

grow than small countries, once the standard effects of the augmented Solow model have


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been taken into account. Does this tell us anything about the effectiveness of aid? Not

directly, though it is surely useful to know that although large countries receive less per

capita aid in relation to per capita income, they have grown just as fast as countries that

have received more, once we take into account the amount that they invest, their levels of

education, and their starting level of GDP. But we would hardly conclude from this fact

alone that aid does not increase growth. Perhaps aid works less well in small countries, or

perhaps there is an offsetting positive effect of population size on economic growth. Both

are possible, and both are worth further investigation. More generally, such arguments

are susceptible to fruitful discussions, not only among economists, but also with other

social scientists and historians who study these questions, something that is typically

difficult with instrumental variable. Economists claims to methodological superiority

based on instrumental variables ring particularly hollow when it is economists themselves

who are often misled. My argument is that for both economists and non-economists, the

direct consideration of the reduced form is likely to generate productive lines of enquiry.

The case of the Egypt instrument is somewhat different. Once again the reduced

form is useful (Egypt doesnt grow particularly fast in spite of all the aid it gets after

Camp David), though mostly for making it immediately clear that the comparison of

Egypt versus non-Egypt, or francophone versus non-francophone, is not a useful way of

assessing the effectiveness of aid on growth. Yet almost every paper in this literature

unquestioningly uses the Egypt dummy as an instrument.

I conclude this section with an example that helps bridge the gap between analyses of

the macro and analyses of the micro effects of aid. Many microeconomists agree that

instrumentation in cross-country regressions is unlikely to be useful, while claiming that


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microeconomic analysis is capable of doing better. We may not be able to answer ill-

posed questions about the macroeconomic effects of foreign assistance, but we can surely

do better on specific projects and programs. Banerjee and He (2008) have provided a list

of the sort of studies that they like and that they believe should be replicated more

widely. One of these, also endorsed by Duflo (2004), is a famous paper by Angrist and

Lavy (1999) on whether schoolchildren do better in smaller classes, a position frequently

endorsed by parents and teachers unions, but not always supported by empirical work.

The question is an important one for development assistance, because smaller class sizes

cost money, and are a potential use for foreign aid. Angrist and Lavys paper uses a

natural experiment, not a real one, and relies on IV estimation, so it provides a bridge

between the relatively weak natural experiments in this section, and the actual

randomized controlled trials in the next.

Angrist and Lavys study is about the allocation of children enrolled in a school into

classes. Many countries set their class sizes to conform to some version of Maimonides

Rule, which sets a maximum class size, beyond which additional teachers must be found.

In Israel, the maximum class size is set at 40. If there are less than 40 children enrolled,

they will all be in the same class. If there are 41, there will be two classes, one of 20, and

one of 21. If there are 81 or more children, the first two classes will be full, and more

must be set up. Angrist and Lavys Figure 1 plots actual class size and Maimonides rule

class size against the number of children enrolled; this graph starts off running along the

45-degree line, and then falls discontinuously to 20 when enrollment is 40, increasing

with slope of 0.5 to 80, falling to 27.7 (80 divided by 3) at 80, rising again with a slope of

0.25, and so on. They show that actual class-sizes, while not exactly conforming to the


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rule, are strongly influenced by it, and exhibit the same saw-tooth pattern. They then plot

test scores against enrollment, and show that they display the opposite pattern, rising at

each of the discontinuities where class-size abruptly falls. This is a natural experiment,

with Maimonides rule inducing quasi-experimental variation, and generating a predicted

class size for each level of enrolment which serves as an instrumental variable in a

regression of test scores on class size. These IV estimates, unlike the OLS estimates,

show that children in smaller class sizes do better.

Angrist and Lavys paper, the creativity of its method, and the clarity and

convincingness of its result has set the standard for micro empirical work since it was

published, and it has had a far-reaching effect on subsequent empirical work in labor and

development economics. Yet there is a problem, which has become apparent over time.

Note first the heterogeneity; it is improbable that the effect of lower class size is the same

for all children so that, under the assumptions of the LATE theorem, the IV estimate

recovers a weighted average of the effects for those children who are shifted by

Maimonides rule from a larger to a smaller class. Those children might not be the same

as other children, which makes it hard to know how useful the numbers might be in other

contexts, for example when all children are put in smaller class sizes. The underlying

reasons for this heterogeneity are not addressed in this quasi-experimental approach. To

be sure of what is happening here, we need to know more about how different children

finish up in different classes, which raises the possibility that the variation across the

discontinuities may not be orthogonal to other factors that affect test scores.

A recent paper by Urquiola and Verhoogen (2008) explores how it is that children are

allocated to different class sizes in a related, but different, situation in Chile where a


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version of Maimonides rule is in place. Urquiola and Verhoogen note that parents care a

great deal about whether their children are in the 40 child class or the 20 child class, and

for the private schools they study, they construct a model in which there is sorting across

the boundary, so that the children in the smaller classes have richer, more educated

parents than the children in the larger classes. Their data match such a model, so that at

least some of the differences in test scores across class size come from differences in the

children that would be present whatever the class-size. This paper is an elegant example

of why it is so dangerous to make inferences from natural experiments without

understanding the mechanisms at work.

In preparation for the next section, I note that the problem here is notthe fact that we

have a quasi-experiment rather than a real experiment, so that there was no actual

randomization. If children had been randomized into class size, the problems would have

been the same, unless there had been some mechanism for forcing the children (and their

parents) to accept the assignment.

4. Randomization in the tropics

Skepticism about econometrics, doubts about the usefulness of structural models in

economics, and the endless wrangling over identification and instrumental variables, has

led to a search for alternative ways of learning about development. There has also been

frustration with the World Banks apparent failure to learn from its own projects, and its

inability to provide a convincing argument that its past activities have enhanced

economic growth and poverty reduction. Past development practice is seen as a

succession of fads, with one supposed magic bullet replacing anotherfrom planning to


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infrastructure to human capital to structural adjustment to health and social capital to the

environment and back to infrastructurea process that seems not to be guided by

progressive learning. For many economists, and particularly for the group at the Poverty

Action Lab at MIT, the solution has been to move towards randomized controlled trials

of projects, programs and policies. RCTs are seen as generating gold standard evidence

that is superior to econometric evidence, and that is immune to the methodological

criticisms that have been characteristic of econometric analyses. Another aim of the

program is to persuade the World Bank to replace its current evaluation methods with

RCTs; Duflo (2004) argues that randomized trials of projects would generate knowledge

that could be used elsewhere, an international public good. Banerjee (2007, Chapter 1)

accuses the Bank of lazy thinking, of a resistance to knowledge, and notes that its

recommendations for poverty reduction and empowerment show a striking lack of

distinction made between strategies founded on the hard evidence provided by

randomized trials or natural experiments and the rest. In all this there is a close parallel

with the evidence-based movement in medicine that preceded it, and the successes of

RCTs in medicine are frequently cited. Yet the parallels are almost entirely rhetorical,

and there is little or no reference to the dissenting literature, as surveyed for example in

Worrall (2007) who documents the rise and fall in medicine of the rhetoric used by

Banerjee. Nor is there any recognition of the many problems of medical RCTs.

The movement in favor of RCTs is currently very successful. The World Bank is now

conducting substantial numbers of randomized trials, and the methodology is sometimes

explicitly requested by governments, who supply the World Bank with funds for this

purpose (see World Bank, 2008 for details of the Spanish Trust Fund for Impact


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Evaluation). There is a new International Initiative for Impact Evaluation which seeks to

improve the lives of poor people in low- and middle-income countries by providing, and

summarizing, evidence of what works, when, why and for how much, (International

Initiative for Impact Evaluation, 2008). The Poverty Action Lab lists dozens of

completed and ongoing projects in a large number of countries, many of which are

project evaluations. Many development economists would subscribe to the jingoist view

proclaimed by the editors of theBritish Medical Journal (quoted by Worrall, 2007)

which noted that Britain has given the world Shakespeare, Newtonian physics, the

theory of evolution, parliamentary democracyand the randomized trial.

4.1 The ideal RCT

Under ideal conditions, and when correctly executed, an RCT can estimate certain

quantities of interest with minimal assumptions, thus absolving RCTs of one complaint

against econometric methods, that they rest on often implausible economic models. It is

useful to lay out briefly the (standard) framework for these results, originally due to Jerzy

Neyman in the 1920s, currently often referred to as the Holland-Rubin framework or the

Rubin causal model, see Freedman (2006) for a discussion of the history. According to

this, each member of the population under study, labeled i, has two possible values

associated with it,0i

Y and1i

Y , which are the outcomes that i would display if it did not

get the treatment, 0,iT = and if it did get the treatment, 1.iT = Since each i is either in the

treatment group or in the control group, we observe one of 0iY and 1iY , but not both. We

would like to know something about the distribution over i of the effects of the treatment,

1 0 ,i iY Y in particular its mean 1 0.Y Y In a sense, the most surprising thing about this set-


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up is that we can say anything useful at all, without further assumptions, or without any

modeling. But that is the magic that is wrought by the randomization.

What we can observe in the data is the difference between the average outcome in the

treatments and the average outcome in the controls, or ( | 1) ( | 0)i i i iE Y T E Y T = = . This

difference can be broken up into two terms

1 0 1 0

0 0

( | 1) ( | 0) [ ( | 1) ( | 1)]

[ ( | 1) ( | 0)]

i i i i i i i i

i i i i

E Y T E Y T E Y T E Y T

E Y T E Y T

= = = = =

+ = =(10)

Note that on the right hand side the second term in the first square bracket cancels out

with the first term in the second square bracket. But the term in the second square bracket

is zero by randomization; the non-treatment outcomes, like any other characteristic, are

identical in expectation in the control and treatment groups. We can therefore write (10)

1 0 1 0( | 1) ( | 0) [ ( | 1) ( | 1)]i i i i i i i iE Y T E Y T E Y T E Y T = = = = = (11)

so that the difference in the two observable outcomes is the difference between the

average treated outcome and the average untreated outcome in the treatment group. The

last term on the right hand side would be unobservable in the absence of randomization.

We are not quite done. What we would like is the average of the difference, rather

than the difference of averages that is currently on the right-hand side of (11). But the

expectation is a linear operator, so that the difference of the averages is identical to the

average of the differences, so that we reach, finally

1 0 1 0( | 1) ( | 0) ( | 1)i i i i i i iE Y T E Y T E Y Y T = = = = (12)

The difference in means between the treatments and controls is an estimate of the average

treatment effect among the treated which, since the treatment and controls differ only by


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randomization, is an estimate of the average treatment effect for all. This standard but

remarkable result depends both on randomization and on the linearity of expectations.

One immediate consequence of this derivation is a fact that is often quoted by critics

of RCTs, but is often ignored by practitioners, at least in economics: RCTs are

informative about the mean of the treatment effects, 1 0i iY Y , but do not identify other

features of the distribution. For example, the median of the difference is not the

difference in medians, so an RCT is not, by itself, informative about the median treatment

effect, something that could be of as much interest to policy makers as the mean

treatment effect. It might also be useful to know the fraction of the population for which

the treatment effect is positive, which once again is not identified from a trial. Put

differently, the trial might reveal an average positive effect although nearly all of the

population is hurt with a few receiving very large benefits, a situation that cannot be

revealed by the RCT, although it might be disastrous if implemented. Indeed, Kanbur

(2002) has argued that much of the disagreement about development policy is driven by

differences of this kind. Given the minimal assumptions that go into an RCT, it is not

surprising that it cannot tell us everything that we would like to know. Heckman and

Smith (1995) discuss these issues at greater length, and also note that, in some

circumstances, more can be learned. Essentially, the RCT gives us two marginal

distributions, from which we would like to infer a joint distribution; this is impossible,

but the marginal distributions limit the joint distribution in a way that can be useful, for

example if the distribution among the treated stochastically dominates the distribution

among the controls.


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In practice, researchers who conduct randomized controlled trials often do present

results on statistics other than the mean. For example, the results can be used to run a

regression of the form

0 1i i j ij j ij i i

j j

Y T X X T u = + + + + (13)

where Tis a binary variable that indicates treatment status, and theXs are various

characteristics measured at baseline that are included in the regression both on their own

(main effects) and as interactions with treatment status, see de Mel, McKenzie, and

Woodruff (2008) for an example of a field experiment with micro-enterprises in Sri

Lanka. The estimated treatment effect now varies across the population, so that it is

possible, for example, to estimate whether the average treatment effect is positive or

negative for various subgroups of interest. These estimates depend on more assumptions

than the trial itself, in particular on the validity of running a regression like (13), on

which I shall have more to say below. One immediate charge against such a procedure is

data mining. A sufficiently determined examination of any trial will eventually reveal

some subgroup for whom the treatment yielded a significant effect of some sort, and

there is no general way of adjusting standard errors to protect against the possibility. In

drug trials, the FDA rules require that analytical plans be submitted prior to trial, and at

least one economic experimentmoving to opportunityhas imposed similar rules on

itself, see the protocol by Feins and McInnis (2001).

I am not arguing against post-trial subgroup analysis, only that any special epistemic

status (as in gold standard, hard, or rigorous evidence) possessed by RCTs does

not extend to subgroup analysis if only because there is no general guarantee that a new

RCT on post-experimentally defined subgroups will yield the same result. Yet such


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analyses do not share any special evidential status that might be accorded to RCTs, and

must be assessed in exactly the same way as we would assess any non-experimental or

econometric study. These issues are wonderfully exposed by the subgroup analysis of

drug effectiveness by Horwitz et al (1996), criticized by Altmann (1998), who refers to

such studies as a false trail, Senn and Harrell (1997), wisdom after the event, and by

Davey Smith and Egger (1998), incommunicable knowledge, drawing the response

reaching the tunnel at the end of the light, by Horwitz et al (1997). It is clearly absurd

to discard data because we do not know how to analyze it with sufficient purity. Indeed,

many important findings have come from post-trial analysis of experimental data, both in

medicine and in economics, for example of the negative income tax experiments of the

1960s. None of which resolves the concerns about data-mining. In large-scale, expensive,

trials, a zero or very small result is unlikely to be welcome, and there is likely to be

overwhelming pressure to search for some subpopulation that gives a more palatable

result.

The mean treatment effect from an RCT may be of limited value for a physician or a

policymaker contemplating specific patients or policies. A new drug might do better than

a placebo in an RCT, yet a physician might be entirely correct in not prescribing it for a

patient whose characteristics, according to the physicians theory of the disease, might

lead her to suppose that the drug would be harmful. Similarly, if we find that dams in

India do not reduce poverty on average, as in Duflo and Pandes fine (non-experimental)

2007 study, there is no implication about any specific dam, even one of the dams

included in the study, yet it is always a specific dam that a policy maker has to decide

about. Their evidence certainly puts a higher burden of proof on those proposing a new


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dam, as would be the case for a physician prescribing in the face of an RCT, though the

force of the evidence depends on the size of the mean effect and the extent of the

heterogeneity in the responses. As was the case with the material discussed in Sections 2

and 3, heterogeneity poses problems for the analysis of RCTs, just as it posed problems

for non-experimental methods that sought to approximate randomization. For this reason,

in his Planning of Experiments, Cox (1958, p.15) begins his book with the assumption

that the treatment effects are identical. He notes that the RCT will still estimate the mean

treatment effect with heterogeneity, but argues that such estimates are quite misleading,

citing the example of two different subgroups within which the treatment effects are

identical, so that the RCT delivers an estimate that applies to no one. This

recommendation makes a good deal of sense when the experiment is being applied to the

parameter of a well-specified model, but it could not be further away from most current

practice in either medicine or economics.

One of the reasons why subgroup analysis is so hard to resist is that researchers,

however much they may wish to escape the straitjacket of theory, inevitably have some

mechanism in mind, and some of those mechanisms can be tested on the data from the

trial. Such testing, of course, does not satisfy the strict evidential standards that the

RCT has been set up to satisfy, and if the investigation is constrained to satisfy those

standards, no ex post speculation is permitted. Without a prior theory, and within its own

evidentiary standards, an RCT targeted at finding out what works, is not informative

about mechanisms. For example, when two independent but identical RCTs in two cities

in India find that childrens scores improved less in Mumbai than in in Vadodora, the

authors state this is likely related to the fact that over 80% of the children in Mumbai


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had already mastered the basic language skills the program was covering, Duflo,

Glennerster, and Kremer (2008). It is not clear how likely is established here, and there

is certainly no evidence that conforms to the gold standard that is seen as one of the

central justifications for the RCTs. For the same reason, repeated successful replications

of a what works experiment is both unlikely and unlikely to be persuasive. Learning

about theory, or mechanisms, requires that the investigation be targeted towards that

theory, towards why something works, not whetherit works. Projects can rarely be

replicated, though the mechanisms underlying success or failure will often be replicable

and transportable. This means that if the World Bank had indeed randomized all of its

past projects, it is unlikely that the cumulated evidence would contain the key to

economic development.

Cartwright (2007a) summarizes the benefits of RCTs relative to other forms of

evidence. In the ideal case, if the assumptions of the test are met, a positive result

implies the appropriate causal conclusion, that the intervention worked and caused a

positive outcome. She adds the benefit that the conclusions follow deductively in the

ideal case comes with great cost: narrowness of scope, (p. 11).

4.2 Tropical RCTs in practice

How well do actual RCTs approximate the ideal? Are the assumptions generally met in

practice? Is the narrowness of scope a price that brings real benefits, or is the superiority

of RCTs largely rhetorical? As always, there is no substitute for examining each study in

detail, and there is certainly nothing in the RCT methodology itself that grants immunity


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from problems of implementation. Yet there are a number of general points that are worth

discussion.

The first is the seemingly obvious practical matter of how to compute the results of a

trial. In theory this is straightforward, we simply compare the mean outcome in the

experimental group with the mean outcome in the control group, and the difference is the

causal effect of the intervention. This simplicity, compared with the often baroque

complexity of econometric estimators, is seen as one of the great advantages of RCTs,

both in generating convincing results, and in explaining those results to policy makers

and the lay public. Yet any difference is not useful without a standard error, and the

calculation of the standard error is rarely quite so straightforward. As Fisher (1935)

emphasized from the very beginning, in his famous discussion of the tea lady,

randomization plays two separate roles. The first is to guarantee that the probability law

governing the selection of the control group is the same as the probability law governing

the selection of the experimental group. The second is to provide a probability law that

enables us to judge whether a difference between the two groups is significant. In his tea

lady example, Fisher uses combinatoric analysis to calculate the exact probabilities of

each possible outcome, but in practice this is rarely done.

Duflo, Glennerster and Kremer (2008, p.3921) (DGK) explicitly recommend what

seems to have become the standard method in the development literature, which is to run

a restricted version of the regression (13), including only the constant and the treatment

dummy,

0 1i i iY T u = + + (14)


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As is easily shown, the OLS estimate of1 is simply the difference between the mean of

the iY in the experimental and control groups, which is exactly what we want. However,

the standard errorfrom the OLS regression is not correct unless the variance in the

experimental group is identical to the variance in the control group, which will only be

true if the treatment has no effect on the variance, which will not generally be the case

particularly if treatment responses are heterogeneous. (Indeed, assuming that the

experiment does notaffect the variance is very much against the minimalist spirit of

RCTs.) If the regression (14) is run with the standard heteroskedasticity correction to the

standard error, the result will be the same as the formula for the standard error of the

difference between two means, but not otherwise unless there are equal numbers of

experimental and controls, in which case the correction makes no difference, and the

OLS standard error is correct. It is not clear in the experimental development literature

whether the correction is routinely done in practice, and the handbook review by DGK

makes no mention of it, although it provides a thoroughly useful review of many other

aspects of standard errors.

Even with the correction for unequal variances, we are not quite done. The general

problem of testing the significance of the differences between the means of two normal

populations with different variances is known as the Fisher-Behrens problem. The test

statistic computed by dividing the difference in means by its estimated standard error

does not have the tdistribution when the variances are different, and the significance of

the estimated difference in means is likely to be overstated if no correction is made. If

there are equal numbers of treatments and controls, the statistic will be approximately

distributed as Students t, but with degrees of freedom that can be as little as half the


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nominal degrees of freedom when one of the two variances is zero. In general, there is

also no reason to suppose that the heterogeneity in the treatment effects is normal, which

will further complicate inference in small samples.

Another standard practice, recommended by DGK, and which is also common in

medical RCTs according to Freedman (2008), is to run the regression (14) with additional

controls taken from the baseline data, or equivalently (13) with thei

X but without the

interactions,

0 1i i j ij i

j

Y T X u = + + + (15)

The standard argument is that, if the randomization is done correctly, the iX are

orthogonal to the treatment variablei

T so that their inclusion does not affect the estimate

of1 , which is the parameter of interest. However, by absorbing variance, as compared

with (14), they will increase the precision of the estimatethis is not necessarily the

case, but will often be true. DGK, p. 3924 give an example controlling for baseline test

scores in evaluations of educational interventions greatly improves the precision of the

estimates, which reduces the cost of these evaluations when a baseline test can be

conducted.

There are two problems with this procedure. The first, which is noted by DGK, is

that, as with post-trial subgroup analysis, there is a risk of data miningtrying different

control variables until the experiment worksunless the control variables are specified

in advance. Again, it is hard to tell whether or how often this dictum is observed. The

second problem is analyzed by Freedman (2008), who notes that (15) is not a standard

regression because of the heterogeneity of the responses. Write i for the (hypothetical)


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treatment response of unit i, so that, in line with the discussion in the previous

subsection, 1 0i i iY Y = , and we can write the identity

0 0 0 0( )

i i i i i i iY Y T Y T Y Y = + = + + (16)

which looks like the regression (15) with theXs and the error term capturing the

variation in0.

iY The only difference is that the coefficient on the treatment term has an i

suffix because of the heterogeneity. If we define ( | 1)i iE T = = , the average treatment

effect among the treated, as the parameter of interest, as in Section 4.1, we can rewrite

(16) as

0 0 0( ) ( )i i i i iY Y T Y Y T = + + + (17)

Finally, and to illustrate, suppose that we model the variation in0i

Y as a linear function of

an observable scalar0iX and a residual i , we have

0 ( ) [ ( ) ]i i i i i iY T X X T = + + + + (18)

with0 0Y = , which is in the regression form (15), but allows us to see the links with the

experimental quantities.

Equation (18) is analyzed in some detail by Freedman (2008). It is easily shown that

iT is orthogonal to the compound error, but that this is not true of .

iX X (Nor will it be

true of the interaction terms in equation 15). However, the two right hand side variables

are uncorrelated because of the randomization, so the OLS estimate of1 is consistent.

This is not true of , though this may not be a problem if the aim is to reduce the

sampling variance. A more serious issue is that the dependency betweeni

T and the

compound error term means that the OLS estimate is biased, and in small samples this


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biaswhich comes from the heterogeneitymay be substantial. Freedman notes that the

leading term in the bias of the estimate of the OLS estimate of is /n where n is the

sample size and

2

1

1lim ( )( )

n

i i

i

X Xn

=

= (19)

Equation (19) shows that the bias comes from the heterogeneity, or more specifically,

from a covariance between the heterogeneity in the treatment effects and the squares of

the included covariates. With the sample sizes typically encountered in these

experiments, which are often expensive to conduct, the bias can be substantial. One

possible strategy here would be to compare the estimates of with and without

covariates; even ignoring pre-test bias, it is not clear how to make such a comparison

without a good estimate of the standard error. Another possibility is to introduce the

interactions between the covariates and the treatment, which leads back to (13). An

incomplete analysis suggests that this might reduce the bias compared with (19).

Of these and related issues in medical trials, Freedman writes Practitioners will

doubtless be heard to object that they know all this perfectly well. Perhaps, but then why

do they so often fit models without discussing assumptions?

All of the issues so far can be dealt with, either by appropriately calculating standard

errors, or by refraining from the use of covariates, though this might involve drawing

larger and more expensive samples. However, there are other practical problems that are

harder to fix. One of these is that subjects may fail to accept assignment, so that people

who are assigned to the experimental group may refuse, and controls may find a way of

getting the treatment, and either may drop out of the experiment altogether. The classical

remedy of double blinding, so that neither the subject nor the experimenter know which


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subject is in which group, is rarely feasible in social experimentschildren know their

class sizeand is often not feasible in medical trialssubjects may decipher the

randomization, for example by asking a laboratory to check that their medicine is not a

placebo. Heckman (1992) notes that, in contrast to people, plots of grounds do not

respond to anticipated treatments of fertilizer, nor can they excuse themselves from being

treated. This makes the important point, further developed by Heckman in later work,

that the deviations from assignment are almost certainly purposeful, at least in part. The

people who struggle to escape their assignment will do so more vigorously the higher are

the stakes, so that the deviations from assignment cannot be treated as random

measurement error, but will compromise the results in fundamental ways.

Once again, there is a widely-used technical fix, which is to run regressions like (15)

or (18), with actual treatment status in place of the assignedtreatment status iT. This

replacement will destroy the orthogonality between treatment and the error term, so that

OLS estimation will no longer yield a consistent estimate of the average treatment effect

among the treated. However, the assigned treatment status, which is known to the

experimenter, is orthogonal to the error term, and is correlated with the actual treatment

status, and so can serve as an instrumental variable for the latter. But now we have come

all the way back to the discussion of instrumental variables in Section 2, and we are

doing econometrics, not an ideal RCT. Under the assumption of no defierspeople

who do the opposite of their assignment just because of the assignment (and it is not clear

just why are there no defiers, Freedman, 2006)the instrumental variable converges to

the local average treatment effect (LATE). As before, it is unclear whether this is what

we want, and there is no way to find out without modeling the behavior that is


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responsible for the heterogeneity of the response to assignment, as in the local

instrumental variable approach developed by Heckman and his coauthors, Heckman and

Vytlacil (1999, 2007). Alternatively, and as recommended by Freedman (2004, p. 4,

2006), it is always informative to make a simple unadjusted comparison of the average

outcomes between treatments and controls according to the original assignment. This

may also be enough if what we are concerned with is whether the treatment works or not,

rather than with the size of the effect. In terms of instrumental variables, this is a

recommendation to look at the reduced form, and again harks back to similar arguments

in Section 2 on aid effectiveness.

There is also a host of operational problems that afflict every actual experiment; these

can be mitigated by careful planningin RCTs compared with econometric analysis,

most of the work is done before data collection, not afterbut not always eliminated. In

this context, I turn to the flagship study of the new movement in development economics,

Miguel and Kremers (2004) study of intestinal worms in Kenya. This paper is repeatedly

cited in DGKs manual, and it is one of the exemplary studies cited by Duflo (2004) and

by Banerjee and He (2008). It was written by two senior authors at leading research

universities, and published in the most prestigious technical journal in economics. It has

also received a great deal of positive attention in the popular press, see for example

Leonhardt (2008), and has been influential in policy, see Poverty Action Lab (2007). In

this study, a group of seventy-five rural primary schools were phased into treatment in a

randomized order, with the finding that the program reduced school absenteeism by at

least one quarter, with particularly large participation gains among the youngest children,

making deworming a highly effective way to boost school participation among young


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children (p. 159). The point of the RCT is less to show that deworming medicines are

effective, but because children infect one another, that school-based treatment is more

effective than individual treatment. As befits a paper that aims to change methods as well

as practice, there is emphasis on the virtues of randomization, and the word random or

its derivatives appears some 60 times in the paper. But the actual method of

randomization is not precisely described in the paper, and private communication with

Michael Kremer has confirmed that, in fact, the local partners would not permit the use of

random numbers for assignment, so that the assignment of schools to three groups was

done in alphabetical order, as in Albert to group 1, Alfred to group 2, Bob to group 3,

Charles to group 1 again, David to group 2, and so on. Alphabetization, not

randomization, was also used in the experiment on flip charts in schools by Glewwe,

Kremer, Moulin, and Zitzewitz (2004); this paper, like Worms, is much cited as

evidence in favor of the virtues of randomization.

Alphabetization may be a reasonable solution when randomization is impossible, but

we are then in the world of quasi- or natural experiments, not randomized experiments.

As is true with all forms of quasi-randomization, alphabetization does not guarantee

orthogonality with potential confounders. Resources are often allocated alphabetically,

because that is how many lists are presented, and it is easy to imagine that the Kenyan

government or local NGOs, like Miguel and Kremer, used the alphabetical list to

prioritize projects or funding. If so, schools higher in the alphabet are systematically

different, and this difference will be inherited in an attenuated form by the three groups.

Indeed, this sort of contamination is described by Cox (1958, 745) who explicitly warns

against this sort of convenient design. Of course, it is also possible that the


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alphabetization causes no confounding with factors known or unknown. If so, there is

still an issue with the calculation of standard errors. Without a probability law, we have

no way of discovering whether the difference between treatments and controls could have

risen by chance. We might think of modeling the situation here by imagining that the

assignment was equivalent to taking a random starting value and assigning every third

school to treatment. If so, the fact that there are only three possible assignments of

schools would have to be taken into account in calculating the standard errors, and

nothing of this kind is reported. As it is, it is impossible to tell whether the experimental

differences in these studies are or are not due to chance.

In the subsection, I have dwelt on practice not to critique particular studies or

particular results; indeed it seems entirely plausible that deworming is a good idea, and

that the costs are low relative to other interventions. My main point here is different, that

conducting good RCTs is difficult and often expensive, so that problems often arise that

need to be dealt with by various econometric or statistical fixes. There is nothing wrong

with such fixes in principlethough they often compromise the substance, as in the

instrumental variable estimation to correct for failure of assignmentbut their

application takes us out of the world of ideal RCTs, and back into the world of everyday

econometrics and statistics. So that RCTs, although frequently useful, are not exempt

from the routine statistical and substantive scrutiny that should be routinely applied to

any empirical investigation.

Although it is well beyond my scope in this paper, I should note that are RCTs in

medicinethe gold standard to which development RCTs often compare themselves

are not exempt from practical difficulties, and their primacy is not without challenge. In


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particular, ethical (human subjects) questions surrounding RCTs in medicine have

become sufficiently severe to seriously limit what can be undertaken. At the same time

there is much concern that those who sponsor trials and those who analyze them have

large financial stakes in the outcome, which sometimes casts doubts on the results. This is

not currently a problem in economics, but would surely become one if, as the advocates

argue, RCTs became a precondition for funding of projects. Beyond that Concato et al

(2000) argue that, in practice, RCTs do not provide useful information beyond what can

be learned from well-designed and carefully interpreted observational studies.

5. Where should we go from here?

Cartwright (2007b) maintains a useful distinction between hunting causes and using

them, and this Section is about the use of randomized controlled trials for policy. This

raises the issue of generalizability or external validityas opposed to internal validity as

discussed in the previous sectiongrounds on which development RCTs are sometimes

criticized, see for example Rodrik (2008).

There are certainly cases in both medicine and economics where an RCT has had a

major effect on the way that people think. In the recent development literature, my

favorite is Chattopadhyay and Duflos (2004) study of women leaders in India. Some

randomly selectedpanchayats were forced to have female leaders, and the paper explores

the differences in outcomes between such villages and others with male leaders. There is

a theory (of sorts) underlying these experiments; the development community had for a

while adopted the view that a key issue in development was the empowerment of women

(or perhaps just giving them voice), and if this was done, more children would be


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educated, more money would be spent on food and on health, and many other socially

desirable outcomes. Women are altruistic and men are selfish. Chattopadhyay and

Duflos analysis of the Indian governments experiments shows that this is wrong. There

are many

instruments of development: randomization in the tropics,

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